13.5 Phase Changes

Phase Changes and Equilibrium

Phase diagrams show how matter behaves under different combinations of temperature and pressure. They map out when a substance exists as a solid, liquid, or gas, and they reveal the exact conditions where phase changes occur. Understanding these diagrams is key to predicting how substances will behave in everything from industrial processes to weather systems.

This section also covers Dalton's law of partial pressures, the triple point, and the energy involved in phase transitions.

Interpretation of Phase Diagrams

A phase diagram is a graph with pressure on the vertical axis and temperature on the horizontal axis. The diagram is divided into regions representing solid, liquid, and gas phases, with curves (called phase boundaries) separating them. Any point on a boundary curve represents conditions where two phases coexist in equilibrium.

There are three boundary curves to know:

• Sublimation curve separates the solid and gas regions. Along this line, a solid can convert directly to gas (or vice versa). Dry ice (solid $CO_2$) sublimating at atmospheric pressure is a classic example.
• Melting (fusion) curve separates the solid and liquid regions. Cross this line and a solid melts into a liquid, or a liquid freezes into a solid.
• Vaporization curve separates the liquid and gas regions. This is the line you cross when a liquid boils or a gas condenses.

Two special points appear on every phase diagram:

• Triple point: The specific temperature and pressure where all three phases coexist simultaneously. For water, this occurs at 0.01°C and 611.73 Pa. All three boundary curves meet here.
• Critical point: The temperature and pressure above which you can no longer distinguish between liquid and gas. For water, this is 374°C and 22.06 MPa. Beyond the critical point, the substance becomes a "supercritical fluid."

Dalton's Law of Partial Pressures

When multiple gases share a container, each gas contributes to the total pressure independently. Dalton's law states that the total pressure of a gas mixture equals the sum of the individual partial pressures:

$P_{total} = P_1 + P_2 + ... + P_n$

A gas's partial pressure is the pressure it would exert if it alone filled the entire container at the same temperature. For example, air is roughly 78% nitrogen and 21% oxygen. At standard atmospheric pressure (101,325 Pa), nitrogen's partial pressure is about 79,000 Pa and oxygen's is about 21,300 Pa.

Practical applications include:

• Scuba diving: Divers need to track the partial pressure of each gas in their breathing mixture, because high partial pressures of nitrogen cause narcosis and high partial pressures of oxygen become toxic.
• Respiration: Your lungs exchange gases based on partial pressure differences between the air in your alveoli and your blood.
• Gas mixture analysis: Knowing the total pressure and the percentage composition lets you calculate each component's partial pressure directly.

Triple Point Significance

The triple point deserves its own discussion because it has both practical and conceptual importance.

At the triple point, solid, liquid, and gas phases all exist together in equilibrium. For water, that's 0.01°C and 611.73 Pa. Two things make this significant:

1. It defines the lowest pressure at which liquid can exist. Below 611.73 Pa, water cannot be liquid no matter what temperature you set. Heating ice at very low pressures causes it to sublimate directly to vapor, skipping the liquid phase entirely.
2. It serves as a calibration standard. The triple point of water is used to define the Kelvin temperature scale. One kelvin is defined as 1/273.16 of the thermodynamic temperature of water's triple point.

At the triple point, phase transitions happen without any change in temperature or pressure, as long as all three phases remain present. Energy added or removed simply shifts the proportion of each phase rather than changing the temperature.

Phase Equilibrium Comparisons

Phase equilibrium occurs when the rate of a forward phase transition equals the rate of the reverse transition. At equilibrium, both phases coexist and neither one is growing at the expense of the other.

• Solid-liquid equilibrium (melting/freezing): At the melting point, molecules in the solid and liquid have the same average kinetic energy. The latent heat of fusion is the energy per gram needed to break enough intermolecular bonds to convert solid to liquid. For water, this is 334 J/g. That means melting 1 g of ice at 0°C requires 334 J, all of which goes into overcoming intermolecular forces rather than raising temperature.
• Liquid-gas equilibrium (vaporization/condensation): At the boiling point, molecules in the liquid and gas phases have equal average kinetic energy. The latent heat of vaporization is much larger than the heat of fusion because molecules must fully escape their neighbors. For water, it's 2260 J/g, nearly seven times the heat of fusion.
• Solid-gas equilibrium (sublimation/deposition): During sublimation, molecules jump directly from solid to gas. The latent heat of sublimation equals the sum of the heats of fusion and vaporization, since the molecule must overcome all the same intermolecular forces. For $CO_2$, this is about 573 J/g.

Thermodynamic Concepts in Phase Changes

Three thermodynamic ideas tie into phase transitions:

• Enthalpy change reflects the total energy absorbed or released during a phase transition. Melting and vaporization absorb energy (endothermic), while freezing and condensation release energy (exothermic).
• Entropy increases as a substance moves from solid to liquid to gas. Gas molecules have far more disorder and freedom of motion than molecules locked in a solid crystal. This is why vaporization involves a much larger entropy increase than melting.
• Heat capacity determines how much energy is needed to change a substance's temperature between phase transitions. During a phase change itself, temperature stays constant while energy goes into breaking or forming intermolecular bonds.